- Reasons for numerical scatter and sensitivities
- Influence of spacial and time discretization
- Bifurcations and instability points
- Path following techniques
- Metamodels and Reduced-Order-Modeling
The quality of car crash analysis improved dramatically in the past decade. The simulations include contact, large deformations and non-linear material laws, failure and spot-weld models. However, noisy response of such simulation is a hindrance to full-scale structural optimization, because some resulting quantities change significantly even after tiny changes of geometry or material parameters. Another undesirable feature is sensitivity to numerical options of the models, such as contact algorithm, contact penalty stiffness and time-step.
Reasons for numerical scatter and sensitivities
During crashsimulation comes the solution close to numerous bifurcations points. Each such event is a reason for divergence of solutions bundle. For many systems such divergence has an exponential rate, thus making the system very sensitive.
Bifurcations and instability points
The bifurcation points play important role in dynamical behavior of the system. Detection of them and adequate numerical resolution is important for understanding of predictability of crashsimulation.
Path following techniques
An insight to behavior of the crash may also give a non-linear quasi-static computation. It is much more straightforward to obtain critical points for load-paths than trajectories of dynamical process. It is also possible to compute most undesirable imperfection directions.
Influence of spacial and time discretization
Metamodels and Reduced-Order-Modeling
The study of stability and bifurcation is very expensive. It is quite unrealistic to perform such study on the complete model of a car. However similar instabilities and sensitivities can be already observed for small system. Therefore it is sensible to establish a reduced model from complete by a Metamodel or a Reduced Order Model.